Chapter 17 II Plan & Elevation ENHANCE

CHAPTER 17: PLAN AND ELEVATION

17.1 Key Terms

Orthogonal projection - Unjuran ortogonPlan - PelanFront elevation - Dongakan depanSide elevation - Dongakan sisiFull scale - Skala penuhSolid line - Garis penuh ( used to draw visible edge)

Dashed line - Garis putus-putus (used to draw invisible edge)

Fine solid line - Garis penuh yang halus (used to show projection/ construction line)

Plans and elevations 1

Orthogonal projection on a vertical plane as viewed from the front (X)

Orthogonal projection on a vertical plane as viewed from the side (Y)

Orthogonal projection on a vertical plane as viewed from the top

y

17.2 Orthogonal projectionThe orthogonal projection of an object is a two dimensional or flat image of the object. The image is formed by looking at perpendicular lines, that is , the normal coming from the object and intersecting the plane of view.

Tick ( √ ) the correct orthogonal projections

1 Orthogonal projection on a horizontal plane

2 Orthogonal projection on a horizontal plane

Orthogonal projection on a vertical plane

3 Orthogonal projection on a horizontal plane

Orthogonal projection on a vertical plane

Plans and elevations 2

4

Orthogonal projection on a vertical plane as viewed from the side y

Orthogonal projection on a vertical plane as viewed from the front ,x

17.3 Plan

Plans and elevations 3

y x

The orthogonal projection of a solid on a horizontal plane as viewed from the top of the object is known as plan.

Draw to full scale, the plans of the solids below.

1

2

3

4

5

Plans and elevations 4

The height of the pyramid is 5 cm

6

7

8

9

Plans and elevations 5

10

11

12

17.4 Elevation

Plans and elevations 6

17.4.1 Front Elevation

The orthogonal projection of a solid on a vertical plane as viewed from the front of the object is known as front elevation.

Draw to full scale, the front elevation,(x) of the solids below

1

2

3

4

5

Plans and elevations 7

x

x

x

x

The height of the pyramid is 5 cm

6

7

The height of the prism is 4 cm

8

9

Plans and elevations 8

x

x

x

x

10

11

12

Plans and elevations 9

x

x

x

x

17.4.2 Side Elevation

The orthogonal projection of a solid on a vertical plane as viewed from the side of the object is known as side elevation.

Draw to full scale, the side elevation (Y) of the solids below

1

2

3

4

5

Plans and elevations 10

y

y

y

y

The height of pyramid is 5 cm

6

7

The height of the prism is 3 cm

8

9

Plans and elevations 11

y

y

y

y

5 cm

4 cm

6 cm

10

Plans and elevations 12

y

11

12

Plans and elevations 13

y

y

y

17.4.3 Elevation involving hidden edgesDraw to full scale, the side elevation (Y) of the solids below.

Solid Elevation from yExample :

1

2

3

Plans and elevations 14

y

3 cm5 cm

Radius of the inner cylinder= 1 cmRadius of the outer cylinder= 2 cm

Solid Elevation from y4

5

6

7

Plans and elevations 15

17. 5 Exercises

Example:

Draw to full scale

i. the plan of the solid,ii. the front elevation of the solid as seen from Xiii. the side elevation of the solid as seen from Y

Solution:

(i) (ii) (iii)

Plans and elevations 16

4

6Plan

4 4

73

Elevation x Elevation y

3

6

44

For each of the following solids, draw to full scale

iv. the plan of the solid,v. the front elevation of the solid as seen from X,vi. the side elevation of the solid as seen from Y.

1. A cylinder of radius 2 cm is removed from the centre of a cuboid. The remaining solid is shown in the diagram below.

2

Plans and elevations 17

3

Plans and elevations 18

2 cm

4

Plans and elevations 19

5

Plans and elevations 20

6.

Plans and elevations 21

17.6 Questions according to examination format

Plans and elevations 22

Example : (a)Diagram (i) below shows a solid consisting of a right prism and a right pyramid which are joined at the plane, PQRS. The base, JKLM, is placed on horizontal plane. PJKQ is the uniform cross-section of the prism. PJ and SM are vertical edges. The height of the pyramid is 4 cm. Draw the full-scale elevation of the solid on the vertical plane parallel to JK as viewed from X.

(b) A solid cuboid is joined to the solid in Diagram (i) at the vertical plane, LMSR. The combined solid is shown in Diagram (ii). The square base, JKED, is on a horizontal plane.

Draw the full-scale(i) the plan of the combined solid,(ii) elevation of the combined solid on a vertical plane parallel to LE as viewed from Y

Solution

(a) (b)(i) (b)(ii)

1a

Plans and elevations 23

V

Q/RP/S

K/LJ/M5 cm

3 cm

4 cm

Diagram (i)

Diagram (ii)

G/DH/S/M

F/E

P/J

3 cm

4 cm 1 cm

2 cm

V

K

F/G

E/D

4 cm

1 cm

4 cmK/J

I/H

V

R/SQ/P

3 cm

L/M

The above diagram shows a solid which consists of two prisms whose base ABPQRCD lies on a horizontal table. PU = CV = 6 cm and W is the mid-point of PU. The length of PQ is 7 cm. Draw to full scale, the elevation of the solid on a vertical plane parallel to QR as viewed from Y.

1b

A semi-cylinder is joined to the solid. Draw to full scale,

i. the plan of the solid ii. the elevation the solid on a vertical plane parallel to DR as viewed from x

Plans and elevations 24

Diagram 1(i)

Diagram 1(ii)

2(a). Diagram 2 (i) shows a solid right prism with the rectangular base, PQRS, resting on a horizontal table. EFGHQP is the uniform cross section of the prism. Rectangle EFLM is an inclined plane. Rectangle GHJK is a horizontal plane. EP, FG and HQ are vertical edges.

Draw the full scale plan of the solid.

2(b) A solid cuboid is joined to the prism in Diagram 2(i) at the vertical plane, MSUZ. The combined solid is shown in Diagram 2(ii) . The base PQRUVWS, is on a horizontal plane and AB = BC = 2 cm.

Draw the full scale(i) elevation of the combined solid on a vertical plane parallel to PQ as viewed from X(ii) elevation of the combined solid on a vertical plane parallel to QR as viewed from Y

Plans and elevations 25

Diagram 2 (i)

Diagram 2(ii)

3(a) Diagram 3(i) shows a solid prism with its rectangular base, PQRS, on a horizontal table. The surface, FGKLRQ, is the uniform cross-section of the prism. Rectangle EFGH is an inclined plane and rectangle JKLM is a horizontal plane. FQ, KG and LR are vertical edges.

Draw the full scale elevation of the solid on a vertical plane parallel to QR as viewed from X.

3(b) A solid right prism with the uniform cross-section, ITU, is removed from the solid in Diagram 3(i) . The remaining solid is shown in Diagram 3(ii). Rectangle TFVU is a horizontal plane. IU is a vertical edge. FT = 3 cm and IU = 2 cm.

Draw the full scale (i) plan of the remaining solid(ii) elevation of the remaining solid on a vertical plane parallel to PQ as viewed from Y.

Plans and elevations 26

Diagram 3(i)

Diagram 3(ii)

17.7 Past Year SPM Questions

November 2003

1(a) Diagram 1(i) shows a solid right prism with rectangular base FGPN on a horizontal table. EFGHHJK is the uniform cross-section of the prism. Rectangle EKLM is an inclined plane. Rectangle JHQR is a horizontal plane. EF,KJ and HG are vertical edges.

Draw to full scale the plan of the solid . [3 marks]

(b) A solid cuboid is joined to the prism in the Diagram 1(i).at the vertical plane PQRLMN. The combined solid is as shown in the Diagram 1(ii). The square base FGSW is horizontal.

Draw full scale(i) the elevation of the combined solid on a vertical plane parallel to FG as viewed from C, [ 4 marks ](ii) the elevation of the combined solid on a vertical plane parallel to GPS as viewed from D. [5 marks ]

Plans and elevations 27

Diagram 1(i)

Diagram 1(ii)

July 20042(a) Diagram 4(i) shows a solid right prism with rectangular base ABCD on a horizontal table. The surface ABLKGF is the uniform cross section of the prism. Rectangle EFGH is an inclined plane and rectangle JKLM is a horizontal plane. AF, GK and BL are vertical edges and GK = 2 cm.

Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X. [ 3 marks ]

(b) Another solid right prism is joined to the prism in Diagram 4(i) at the vertical plane CVJQ. The combined solid is as shown in Diagram 4(ii). Quadrilateral PQCW is the uniform cross section of the prism. rectangle WCRU is an inclined plane and the square TPWU is a horizontal plane. The base ABRSQD lies on a horizontal table, KL = JM = 3 cm and GK = 2 cm.

Draw full scale, ( i ) the plan of the combined solid [ 4 marks] ( ii ) the elevation of the combined solid on a vertical plane parallel to BCR as viewed from Y [ 5 marks]

Plans and elevations 28

Diagram 4(i)

Diagram 4(ii)

November 20043(a) Diagram 2(i) shows a solid consisting of a cuboid and a half cylinder which are joined at the plane HJMN. The base GDEF is on a horizontal plane and HJ=3 cm

Draw to full scale, the elevation of the solid on a vertical plane parallel to DG as viewed from X. [3 marks ](b) A solid right prism is joined to the solid in Diagram 2(i) at the vertical plane ELMW. The combined solid is as shown in diagram 2(ii). Trapezium PMWU is the uniform cross-section of the prism and PQRM is an inclined plane. The base DEUTSWFG is on a horizontal plane and EU= 2cm

Draw to full scale,(i) the plan of the combined solid [4 marks](ii) the elevation of the combined solid on a vertical plane parallel to UT as view from Y [5 marks]

Plans and elevations 29

Diagram 2(i)

Diagram 2(ii)

July 2005

4(a) Diagram 5(i) shows a solid right prism with rectangular base ABCD on a horizontal table. The surface ABLKGF is the cross-section of the prism. Rectangle GKJH is an inclined plane. Rectangles JKLM and EFGH are horizontal planes. AF and BL are vertical edges.

Draw full scale, the plan of the solid [ 3 marks]

(b) Another solid cuboid is joined to the prism in Diagram 5(i) at the vertical plane DPJHE. The combined solid is as shown in Diagram 5(ii). The base ABBCPQV lies on a horizontal table.

Draw full scale,( i) the elevation of the combined solid on a vertical plane parallel to BC as viewed from X, [4 marks](ii) the elevation of the combined solid on a vertical plane parallel to AB as viewed from Y. [5 marks]

Plans and elevations 30

Diagram 5(i)

Diagram 5(ii)

November 20055(a) Diagram 3(i) shows a solid right prism with rectangular base PEFN on a horizontal table. The surface EFGHJ is the uniform cross section of the prism. Rectangle KJHL is an inclined plane and rectangle LHGM is a horizontal plane. JE and GF are vertical edges.

Draw full scale, the elevation of the solid on a vertical plane parallel to EF as viewed from X . [ 3 marks ]

(b) A solid right prism with uniform cross section UVWX is removed from the solid in Diagram 3(i). The remaining solid is as shown in Diagram 3(ii) rectangle VSTW is a horizontal plane. UV and XW are vertical edges. VS=3 cm and SE= 2 cm.

Draw full scale, (i) the plan of the remaining solid [ 4 marks] (ii) the elevation of the remaining solid on a vertical plane parallel to PE as viewed from Y .

[ 5 marks]

Plans and elevations 31

Diagram 3(i)

Diagram 3(ii)

July 2006

6. (a) Diagram 7(i) shows a solid right prism with rectangular base ABCD on a horizontal plane. The surface ABHGF is its uniform cross section. The rectangle EFGK is an inclined plane and the square GHJK is a horizontal plane.The edges AF and BH are vertical.

Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X . [ 3 marks ]

(b) Another solid right prism is joined to the solid in Diagram 7(i) at a vertical plane CJKL to form a combined solid as shown in Diagram 7(ii). Trapezium KLMS is its uniform cross section. The rectangle KSRQ is an inclined plane. The edges KL and SM are vertical. The base ABCMNPLD is on a horizontal plane.

Draw to full scale, (i) the plan of the combined solid, [ 4 marks] (ii) the elevation of the combined solid on a vertical plane parallel to ME as viewed from Y.

[ 5 marks]

Plans and elevations 32

SPM Nov 2006

7(a) Diagram 8(i) shows a solid right prism. The surface KLSR is its uniform cross section. The base JKLM is a rectangle on a horizontal plane. The rectangle JKRQ is an inclined plane and the square QRST is a horizontal plane.

The edges SL and TM are vertical.

Draw to full scale, the elevation of the solid on a vertical plane parallel to LK as viewed from X . [ 3 marks ]

(b) Another solid right prism is joined to the solid in Diagram 8(i) at the vertical plane KLSG to form a combined solid as shown in Diagram 8(ii). The trapezium ABCD is its uniform cross section and AFKB is an inclined plane The rectangle ADEF is a horizontal plane. The base JKBCLM is on a horizontal plane. The edge DC is vertical.

Draw to full scale,(i) the elevation of the combined solid on a vertical plane parallel to JB as viewed from Y

[ 4 marks](ii) the plan of the combined solid . [ 5 marks]

Plans and elevations 33

8 SPM Jul 2007 You are not allowed to use graph paper to answer this question. (a) Diagram 6(i) shows a solid right prism with rectangular base FGRQ on a horizontal plane. EFGHJKLM is the uniform cross-section of the prism. Rectangles EMNP, LKUV and JHST are horizontal planes.

FE , LM , KJ and GH are vertical edges. EM = LK = JH = 2 cm.

Draw full scale, the elevation of the solid on a vertical plane parallel to FG as viewed from A.

Plans and elevations 34

Diagram 6(i)

[3 marks]

PN

T

UV

Q

S

R

F

J

E

G

HLK

M

2 cm

6 cm

5 cm

6 cm

3 cm

3 cm

A

(b) Another solid right prism is joined to the solid in Diagram 6(i) at the vertical plane PQRSTUVN . The combined solid is shown in Diagram 6(ii). Right-angled triangle XYZ is its uniform cross-section of the prism.

The base FGRWQ lies on a horizontal plane and FQW is a straighf line.

Draw to full scale,

(i) the plan of the combined solid, (ii) the elevation of the combined solid on a vertical plane parallel to GR as viewed from B .

Plans and elevations 35

[4 marks]

P N

T

UVQ

S

R

F

J

E

G

HLK

M

2 cm

6 cm

5 cm

6 cm

3 cm

3 cm

Y

X

Z

W

3 cm

2 cm

B

Diagram 6(ii)

[5marks]

9 November 2007 You are not allowed to use graph paper to answr this question.

(a) Diagram 7(i) shows a solid right prism with rectanglular base ABCD on a horizontal plane. The surface ABJHGF is the uniform cross- section of the prism. AF , HG and BJ are vertical edges. Rectangle JKLH is a horizontal plane and rectangle GMEF is an inclined plane.

Draw full scale, the plan of the solid.

Plans and elevations 36

[3 marks]

6 cm

5 cm

3 cm

8 cm7 cm

4 cm

A

M

L

D

C

K

E

F

H

G

B

J

Diagram 7(i)

(b) A half-cylinder solid of diameter 6 cm is joined to the prism in Diagram 7(i) at the plane SKLT . The length of SK is 4 cm . The combined solid is shown in Diagram 7(ii).

Draw full scale,

(i) the elevation of the combined solid on a vertical plane parallel to AB as viewed from P ,

(ii) the elevation of the combined solid on a vertical plane parallel to BC as viewed from Q .

Plans and elevations 37

[4 marks]

[5 marks]

Diagram 7(ii)

CA

B

J

K

D

F

LG E

M

T

SH 4 cm

7 cm8 cm

5 cm

P

Q

10 Jun 2008 You are not allowed to use graph paper to answr this question.

(a) Diagram 15(i) shows a solid right prism. The rectanglular base ABCD lies on a horizontal plane. The rectangle ABGF is an inclined plane. Trapezium ADEF is the uniform cross-section of the prism. The edges DE is vertical .

Draw to full scale, the plan of the solid.

Plans and elevations 38

D

C

E

H 3 cm

3 cm

5 cm

5 cm

G

F

A

4cm

[3 marks]

Diagram 15(i)

(b) Another solid right prism is joined to the solid in Diagram 15(i) at the vertical plane DCHE . The composite solid is shown in Diagram 15(ii). Pentagon QPNMR is the cross-section of the prism. PJKN is an

inclined plane and NKLM is a horizontal plane The base ABCSRQD lies on a horizontal plane. The edges RM and QP are vertical.

MN = QD = 2 cm and PQ = 6 cm.

Y

X

Draw to full scale

(i) the elevation of the composite solid on a vertical plane parallel to RQ as viewed from X,

(ii) the elevation of the composite solid on a vertical plane parallel to AB as viewed from Y .

Plans and elevations 39

[4 marks]

[5 marks]

P

L

N

4 cm

K

Q

M

J

D

R

CS

E

H7 cm

4 cm

5 cm

5 cm

G

F

A

B

Diagram 15(ii)

11 November 2008 You are not allowed to use graph paper to answr this question.

(a) Diagram 15(i) shows a solid right prism with rectanglular base ABHG on a horizontal plane.The surface ABCDE is the uniform cross-section of the prism. AE and BC are vertical edges. Rectangle DEFK is an inclined plane and rectangle CDKJ is a horizontal plane.

Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .

Plans and elevations 40

[3 marks]

D CE

H

3 cm

5 cm

6 cm

8 cm

G

F

A

J

4cm

B

K

Diagram 15(i)

X

(b) A solid cuboid is cut and removed from the solid in Diagram 15(i). The remaining solid is shown in Diagram 15(ii). Rectangle QRST is a horizontal plane. SB = 2 cm, UT = 3 cm and ST = 4 cm.

Draw to full scale,

(i) the plan of the remaining solid, (ii) the elevation of the remaining solid on a vertical plane parallel to BH as viewed from Y .

Plans and elevations 41

[4 marks]

DQ

E

H

3 cm

5 cm

6 cm

8 cm

G

F

A

J

4cm

B

K

RS

W U

T

[4 marks]

Y

ANSWERS

Orthogonal projection

Plan Front Elevation, X Side Elevation Y

1 1 1 1

2 2 2 2

3 3 3

3 4 4 4

5 5 5

4 6 6 6

7 7 7

Orthogonal projection

Plan Front Elevation, X Side Elevation Y

1 1 1 1

2 2 2 2

3 3 3

3 4 4 4

5 5 5

Plans and elevations 42

4 6 6 6

7 7 7

8 8 8

9 9 9

10 10 10

11 11 11

12 12 12

17.43 Elevation involving hidden sides1. 2 3 4

5 6 7

Plans and elevations 43

3 cm

5 cm

2 cm

1 cm

1 cm

Plan Front elevation, X Side elevation, Y1

2

3

4

5

Plans and elevations 44

3

2

1

6

1 a.Y-elevation

b.Plan

c.X-elevation

2 (a) (b)(i) (b)(ii)

3

Plans and elevations 45

4 cm

4 cm

6 cm

3 cm

4 cm

6 cm

2 cm

2 cm

4 cm 1 cm

4 cm2 cm

1 cm

3 cm

4 cm

1 cm3 cm 1 cm

1 cm

2 cm

10 cm

4 cm

6 cm

2 cm

6 cm

3 cm3 cm

2 cm

6 cm

2 cm

2 cm

17.7 SPM past years questions

1) SPM2003(N)

1(b)(i)

1(b) (ii)

Plans and elevations 46

5 cm

X/T

G/P/S

2 cm

5 cm

2 cm

V/U

E/M

F/N/W7 cm

J/R

M,N2 cm

R

Q/P

J

H/G

5 cm

5 cm

2 cm

S/WP/NG/F

X//L/V

Q/R

M

T/U

7 cm

K

H/J

E

2 cm

2 cm

3 cm

5 cm 2 cm

2 SPM2004(Julai)

(a) (b) (i)

b(ii)

3 SPM2004(Nov)

(a)

Plans and elevations 47

3 cm

6 cm

2 cm

3 cm

5 cm

6 cm

3 cm

2 cm

4 cm4 cm

6 cm

3 cm2 cm

2cm

4 cm

3 cm

2 cm

4 cm 2cm

7cm

(b) (i)

b(ii)

4 SPM 2005(Julai)

(a)

Plans and elevations 48

P Q

RK/J/HL/M/N

D/GU/E/W/F T/S

3 cm

4 cm

2 cm

2 cm

H/G N/F

J

K/D

M/W

P/U

R/S

L/E

Q/T

3 cm

3 cm

4 cm

5 cm

2 cm

(b) (i)

(ii)

Plans and elevations 49

5 SPM 2005(Nov)

(b)(i)

3 b(ii)

Plans and elevations 50

7 cm

8 cm

4 cm

J,K

H,L G,M

E,P F,N

K,P

U,V

S,E

L M,N

X,W

H,T G,F

K U

L,M

P,N

X H,G

V,WS,T

E,F

6 SPM 2006(Julai)

Plans and elevations 51

7 SPM 2006(Nov)

Plans and elevations 52

SPM 2007(Jun)

SPM 2007(Nov)

Plans and elevations 53

SPM 2008(Jun)

SPM 2008(Nov)

Plans and elevations 54